27 log 8 * 4log125 * 25log1/9 = .... Question from @MimooRemaa

December 2018 2 98 Report

27 log 8 * 4log125 * 25log1/9 = ...

DB45 ²⁷log 8 . ⁴log 125 . ²⁵log ¹/₉ =
= ³^³'log 2³ . ²^²'log 5³. ⁵^²log 3⁻²
= ³/₃ ³log 2. ³/₂ .²log 5 . (⁻²/₂) ⁵log 3
= (³/₃)(³/₂)(-²/₂) ( ³log 2.²log ⁵.⁵log 3)
= - ³/₂ (³log 3)
= - ³/₂ (1)
= - ³/₂

0 votes Thanks 1

Yusrin091 $^{27} log 8 = ^{ 3^{3} } log 2^{3} = ^{3} log 2$
$^{4} log 125 = ^{ 2^{2} } log 5^{3} = \frac{3}{2} . ^{2} log 5$
$^{25} log (1/9) = ^{ 5^{2} } log 3^{-2} = \frac{-2}{2} . ^{5} log 3 = -^{5} log 3$

27 log 8 * 4log 125 * 25log (1/9)
   = 3log 2 * (3/2).2log 5 * (-1).5log 3
   = (-3/2). 2log 5 * 5log 3 * 3log 2
       = (-3/2)* 2log 2
   = (-3/2) * 1
   = -3/2

1 votes Thanks 1

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